{
  "abstract": "We prove that if a minimal ordered structure $(M, <, \\ldots)$ with infinite chains in an arbitrary language extending the language of strict orders interprets (in some power $M^n$) the linear order $(ω, <)$, then this fact can be witnessed for $n=1$ via the incomparability relation of an $<$-definable strict order $R$; that $R$ is unique up to ``almost equality'', i.e., finite rearrangements of elements of $M$; and that $R$ can be defined from $<$ in a constructive way. We also show that several variants of the question whether a minimal ordered structure interprets an infinite linear order are all equivalent.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36313",
  "author_total": 1,
  "authors": [
    {
      "name": "Grzegorz Jagiella"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fnzqgrkr05mn5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36313",
  "fulltext_url": null,
  "id": "fnzqgrkr05mn5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36313",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.LO"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7214965898",
  "pdf_url": "https://arxiv.org/pdf/2609.36313",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fnzqgrkr05mn5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2609.36313",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36313"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "On canonicity of almost linear minimal orders",
  "title_text": "On canonicity of almost linear minimal orders",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/fnzqgrkr05mn5",
  "venue": "arXiv",
  "versions": []
}